Abstract.Applying the notion of relatively maximal -relaxed monotonicity to the approximation solvability of a general class of inclusion problems, a generalization to the investigation of Eckstein and Bertsekas (1992) on the weak convergence using the proximal point algorithm in a real Hilbert space setting is achieved. Further more, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution inclusions.